Matplotlib logit scale tick number formatting

When using the log scale with matplotlib, we can set globally with (see this answer)

import matplotlib.pyplot as plt
plt.rcParams['axes.formatter.min_exponent'] = 3

that ticks on logarithmic axes are in exponential form only for x<1.e-3 and x>1.e3, but in between are just 0.001, 0.01, 0.1, 1, 10, 100, and 1000.

How can I obtain the equivalent behavior with the logit scale of matplotlib?, such that the labels become 0.001, 0.01, 0.1, 0.5, 0.9, 0.99, 0.999?

To do this you can define your own tick formatter, in particular, you can subclass the LogitFormatter to do what you want. Following the logit_demo example, you could do:

import math
from matplotlib.ticker import LogitFormatter
import matplotlib.pyplot as plt
import numpy as np


# create a formatter class based on the LogitFormatter
class NonScientificLogitFormatter(LogitFormatter):
    def __init__(self, *args, **kwargs):
        # set the default range within which it will not use scientific notation
        self.form_range = kwargs.get("normal_format_range", 1e-3)
        
        super().__init__(*args, **kwargs)

    def __call__(self, x, pos=None):
        # if within that range just output the tick location value as a string
        if x >= self.form_range and x <= 1 - self.form_range:
            return str(x)
        else:
            return super().__call__(x, pos=pos)


xmax = 10
x = np.linspace(-xmax, xmax, 10000)
cdf_norm = [math.erf(w / np.sqrt(2)) / 2 + 1 / 2 for w in x]
cdf_laplacian = np.where(x < 0, 1 / 2 * np.exp(x), 1 - 1 / 2 * np.exp(-x))
cdf_cauchy = np.arctan(x) / np.pi + 1 / 2

fig, ax = plt.subplots()

# Common part, for the example, we will do the same plots on all graphs
ax.plot(x, cdf_norm, label=r"$\mathcal{N}$")
ax.plot(x, cdf_laplacian, label=r"$\mathcal{L}$")
ax.plot(x, cdf_cauchy, label="Cauchy")
ax.legend()
ax.grid()

# First line, logitscale, with standard notation
ax.set(title="logit scale")
ax.set_yscale("logit")
ax.set_ylim(1e-5, 1 - 1e-5)

maj_form = ax.yaxis.get_major_formatter()

# set the y-axis formatter to the one we defined
ax.yaxis.set_major_formatter(
    NonScientificLogitFormatter(
        one_half=maj_form._one_half,
        use_overline=maj_form._use_overline
    )
)